Probability of a Positive Score in a Coin Game
Combinatorics · 28th PMO Qualifying Stage
Zoey plays a game in which she flips a fair coin 11 times. For each flip after the first, she gains 1 point if her previous flip was a tail and she flips a head. On the other hand, she loses 1 point if her previous flip was a head and she flips a tail. Otherwise, her score does not change. What is the probability that, at the end of the game, she ends up with a positive score?
A$\dfrac{5}{32}$
B$\dfrac{11}{64}$
C$\dfrac{1}{4}$
D$\dfrac{1}{2}$